Question

If all the letters of the word MESSI are permuted in all possible ways and the words [with or without meaning] thus formed are arranged in dictionary order, then the rank of the word MESSI is

• A. \( 18 \)
• B. \( 27 \)
• C. \( 23 \)
• D. \( 26 \)

Hint:

Always divide by the factorial of the repetition count (\( 2! \) for the two 'S' letters) when calculating permutations of remaining items. Forgetting this division is the most common reason for getting an inflated rank.

Answer 1

The Correct Option is D

Step 1: Sort the letters.
The word MESSI has letters E, I, M, S, S in alphabetical order. Note S repeats twice.
Step 2: Count words starting with E.
Fix E first; the rest I, M, S, S arrange in $\dfrac{4!}{2!} = 12$ ways.
Step 3: Count words starting with I.
Fix I first; the rest E, M, S, S arrange in $\dfrac{4!}{2!} = 12$ ways. So $12+12 = 24$ words come before any starting with M.
Step 4: Start the M words.
Now words begin with M, then we order the rest E, I, S, S alphabetically. The smallest is MEISS, which is the 25th word.
Step 5: Find the next word.
The next arrangement after MEISS, moving the letters forward, is MESSI, the 26th word.
Step 6: State the rank.
So MESSI sits at position \[ \boxed{26} \]